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On linear regression models in infinite dimensional spaces with scalar response

Author

Listed:
  • Andrea Ghiglietti

    (Università degli Studi di Milano)

  • Francesca Ieva

    (Università degli Studi di Milano)

  • Anna Maria Paganoni

    (Politecnico di Milano)

  • Giacomo Aletti

    (Università degli Studi di Milano)

Abstract

In functional linear regression, the parameters estimation involves solving a non necessarily well-posed problem, which has points of contact with a range of methodologies, including statistical smoothing, deconvolution and projection on finite-dimensional subspaces. We discuss the standard approach based explicitly on functional principal components analysis, nevertheless the choice of the number of basis components remains something subjective and not always properly discussed and justified. In this work we discuss inferential properties of least square estimation in this context, with different choices of projection subspaces, as well as we study asymptotic behaviour increasing the dimension of subspaces.

Suggested Citation

  • Andrea Ghiglietti & Francesca Ieva & Anna Maria Paganoni & Giacomo Aletti, 2017. "On linear regression models in infinite dimensional spaces with scalar response," Statistical Papers, Springer, vol. 58(2), pages 527-548, June.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:2:d:10.1007_s00362-015-0710-2
    DOI: 10.1007/s00362-015-0710-2
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    References listed on IDEAS

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    1. Jacques, Julien & Preda, Cristian, 2014. "Model-based clustering for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 92-106.
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